SIGNIFICANT FIGURES AND ROUNDING OFF

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The number of significant figures in any measurement indicates the degree of precision of that measurement. 
The degree of precision is determined by the least count of the measuring instrument.

  • Suppose a length measured by a meter scale  ( of least count = 0.1 cm ) is 1.5 cm, then it has only two significant figures, namely 1 and 5. 
  • Measured with a vernier callipers ( of least count = 0.01 cm ) the same length 1.53 cm and it then has three significant figures.
  • Measured with a screw gauge ( of least count = 0.001 cm ) the same length may be 1.536 cm which has four significant figures. 



  • It must be clearly understood that we cannot increase the accuracy of a measurement by changing the unit.
  •  For example, suppose a measurement of mass yields a value 39.4 kg. It is understood that the measuring instrument has a least count of 0.1 kg.
  •  In this measurement, three figures 3, 9, 4 are significant. If we change 39.4 kg to 39400 g or 39400000 mg, we cannot change the accuracy of measurement. 
  • Hence 39400 g or 39400000 mg still have three significant figures; the zeroes only serve to indicate only the magnitude of measurement.

Estimation of appropriate significant figures in calculations

  • The importance of significant figures lies in calculation to find the result of addition or multiplication of measured quantities having a different number of significant figures.
  • The least accurate quantity determines the accuracy of the sum or product.
  • The result must be rounded off to the appropriate digit.

Rules for rounding off
  1. If the digit to be dropped is less than 5, the next ( preceding ) digit to be dropped is left unchanged. For example, if a number 5.34 is to be rounded off to two figures, the digit to be dropped is 4 which is less than 5.
  2. If the digit to be dropped is more than 5, the preceding digit to be retained is increased by 1. For example, 7.536 is rounded off as 7.54 to three significant figures.
  3. If the digit to be dropped happens to be 5, then the preceding digit to be retained is increased by 1 if it is odd, or
    the preceding digit is retained unchanged if it is even.
    6.75 is rounded off to 6.8 and 4.95 is rounded off to 5.0 but 3.45 is rounded off to 3.4.

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